I am not an American but this has always baffled me. From what I understand, American government is not allowed to compel someone to self incriminate themselves. However, IRS wants people to report their income even if it is illegally obtained. So to me it sounds like the government is forcing citizens to self incriminate themselves by showing "or else" stick dangling over their heads. Always wondered how this conundrum is handled within the legal framework.
You would report illegal income via Schedule 1, line 8. At the bottom, after naming many specific legal sources of income there is a line 8z "Other income. List type and amount" with very little space. The instructions refer you to Miscellaneous Income in Pub 525. They do list "Stolen Property" as a category, saying
If you steal property, you must report its FMV in your income in the year you steal it unless in the same year, you return it to its rightful owner.
However, there is no requirement to report the illegal nature of your income, and it is not difficult to describe such income in non-incriminating terms, such as "miscellaneous income".
If they are not satisfied, you may inform them of your 5th amendment right to not incriminate yourself. Invoking your right to silence does not constitute probable cause for a search warrant.
There is no crime named "obtaining income illegally"
To charge a person who confessed to the above, a prosecutor needs to be much more specific. But the person won't be specific because that would self-incriminate them.
Thus, a mere confession to obtaining income illegally does not self-incriminate: no charges can be laid, let alone proved.